Dzikovskyi D. Generalization of S. Chandrasekhar's model in the theory of massive degenerate dwarfs

The dissertation is devoted to the calculation of internal structure and macroscopic characteristics of degenerate dwarfs by taking into account the main factors in the formation of these stars. New models developed in this work generalize S. Chandrasekhar's standard model. For the first time it was proposed the model of degenerate dwarf with partial spin-polarization of the electron subsystem. It was shown that spin-polarization leads to an increase of mass and radius of degenerate dwarf in comparison with corresponding characteristics of S. Chandrasekhar's standard model. The influence of the axial rotation on characteristics of degenerate dwarfs were investigated. It was established that the axial rotation causes an increase of the dwarfs' mass and deviation of stellar surface shape from spherical symmetry. The approximate solutions of the equilibrium equation of rotating degenerate dwarf were found using numerical integration of the equilibrium equation in partial derivatives, as well as the expansion on the basis of universal functions of the radial variable and Legendre polynomials. The influence of the spin-polarization and the incomplete degeneration of an ideal relativistic electron subsystem on the characteristics of the degenerate dwarfs were studied. It was shown that the influence both of these factors lead to a significant increase of mass and radius in comparison with characteristics of the standard model. The inverse problem was solved and the temperature of the isothermal core and the relativistic parameter in its center were found. It was shown that with increasing impact of spin-polarization the core temperature decreases. In order to construct the equation of state for the degenerate dwarf matter based on the reference system approach it was calculated the energy of ground state of macroscopically homogeneous two-component electron-nuclear model at high densities in the approximation of two- and three-particle electron correlations. The contributions of the main components of the energy to the equation of state of the model were analyzed in the case of crystal structure of the nuclear subsystem. The relative decrease of pressure was investigated as a function of the nuclear charge and the relativistic parameter. It was proposed the method of solving the mechanical equilibrium equation of massive degenerate dwarfs with taking into account the axial rotation and interparticle interactions which are the competing factors. The effects of the general theory of relativity on the dwarf's characteristics were studied in the frame of the model with spin-polarized ideal electron subsystem based on the variational principle. The same calculations were performed using the Oppenheimer - Volkoff equation in the model which takes into account interparticle interactions and axial rotation - the mass of the dwarf was determined as well as the relativistic parameter which corresponds to the onset of the object's instability.